The Rays are now 4-1 in their past five games against the Royals, dating back to last season, following a stretch when they were 1-15 against Kansas City.
C.J. Cron had two hits for the Rays, including a two-run home run two batters into the game. Whit Merrifield had two hits and drove in three runs for the Royals, giving him a multi-hit game on consecutive nights.
Jonny Venters (1-0) pitched two-thirds of an inning for the Rays to earn the victory, while Alex Colome pitched the ninth inning for his eighth save. Kelvin Herrera (1-1) gave up one run on three hits over one inning to take the loss.
Merrifield had a two-run single in the seventh inning off Rays reliever Jose Alvarado to tie the score 5-5 after the Royals had trailed the entire game. Merrifield also had an RBI single in Kansas City's two-run fifth inning.
Rays starter Anthony Banda gave up three runs on six hits without a walk in five innings of his Tampa Bay debut. Banda opened the season in the minor leagues after being acquired in February from the Arizona Diamondbacks in a three-team deal that also included the New York Yankees.
Royals starter Ian Kennedy gave up five runs on seven hits over six innings with six strikeouts and three walks.
After Cron's first-inning home run, his ninth, Adeiny Hechavarria added an RBI single later in the first inning for a 3-0 Tampa Bay lead.
Cron's home run was the Rays' 36th of the season, second lowest in all of baseball, ahead of only the Miami Marlins' 31.
The Royals scored their first run in the second inning on an Alex Gordon RBI groundout, but the Rays regained their two-run lead on an RBI single from Mallex Smith in the third.
Kansas City's Ryan Goins had an RBI in the fifth inning, as did Merrifield, delivering a run-scoring groundout as the Rays' lead was cut to 4-3. Tampa Bay's Jesus Sucre made it a 5-3 lead in the sixth when his suicide squeeze bunt to the right of the pitcher's mound scored Smith.
--Field Level Media